We propose a practical scheme for calculating the local gravitational self-
force experienced by a test mass particle moving in a black hole spacetime.
The method-equally effective for either weak or strong field orbits-employ
s the mode-sum regularization scheme previously developed for a scalar toy
model. The starting point for the calculation. in this approach, is the for
mal expression for the regularized self-force derived by Mino et al. [Phys.
Rev. D 55, 3457 (1997)] (and, independently, by Quinn and Wald [Phys. Rev.
D 56 3381 (1997)]), which involves a worldline integral over the tail part
of the retarded Green's function. This force is decomposed into multipole
(tensor harmonic) modes. whose sum is subjected to a carefully designed reg
ularization procedure. This procedure involves an analytical derivation of
certain "regularization parameters" by means of a local analysis of the Gre
en's function. This paper contains the following main parts: (1) The introd
uction of the mode sum scheme as applied to the gravitational case. (2) Two
simple cases studied: the test case of a static particle in flat spacetime
, and the case of a particle at a turning point of a radial geodesic in Sch
warzschild spacetime. In both cases we derive all necessary regularization
parameters. (3) An analytical foundation is set for applying the scheme in
more general cases. (In this paper, the mode sum scheme is formulated withi
n the harmonic gauge. The implementation of the scheme in other gauges shal
l be discussed in a separate. forthcoming paper.).